1MA1 · N2–N3NumberFoundation & HigherGrades 1–4

The Four Operations

Q: What is -5 - 3?

Start at -5 and move 3 further left: -8.

Adding, subtracting, multiplying and dividing are the first things anyone learns in maths — and on a non-calculator paper they are where marks quietly disappear. This lesson sharpens the written methods, handles negative numbers with confidence, and fixes the order in which a calculation must be done.

45 min Number Fundamentals

The big picture

The four operations come in two inverse pairs: addition undoes subtraction, and multiplication undoes division. Using that relationship is the fastest way to check an answer without a calculator.

Edexcel Paper 1 is non-calculator, so reliable written methods for long multiplication and division are essential, and every multi-step problem depends on applying the order of operations correctly.

What you'll learn

Use written methods for multiplication and division, including with decimals
Add, subtract, multiply and divide with negative numbers
Apply the order of operations, including brackets and powers
Use inverse operations to check calculations

Written multiplication and division

For long multiplication, split one number into place-value parts, multiply each, and add. A grid or column method both work — what matters is that tens are multiplied as tens.

For division, short division (the "bus stop") works for any divisor you can handle mentally. Carry remainders into the next column.

With decimals, ignore the point, calculate with whole numbers, then place the point using an estimate. $2.4 \times 0.3$ : $24 \times 3 = 72$ , and the estimate $2 \times 0.3 = 0.6$ tells you the answer is $0.72$ .

368 \times 20 = 7360

368 \times 4 = 1472

3Add:

7360 + 1472

Answer

8832

Your turnSame method, new numbers — try it before moving on.

Work out $427 \times 36$ without a calculator.

Your answer

Your turnSame method, new numbers — try it before moving on.

Work out $9.12 \div 0.3$ .

Your answer

Tip — Dividing by a decimal is awkward; scaling both numbers by the same power of 10 keeps the answer the same and makes the divisor whole.

Negative numbers

Adding a negative is the same as subtracting: $5 + (- 8) = 5 - 8 = - 3$ . Subtracting a negative is the same as adding: $4 - (- 6) = 10$ .

For multiplication and division, work out the size first, then the sign: same signs give a positive answer, different signs give a negative.

Temperatures, bank balances and floors below ground make good checks: a temperature of $- 3$ °C that rises by $7$ degrees reaches $4$ °C.

(- 6) \times (- 4) = 24

(same signs).

18 \div (- 3) = - 6

(different signs).

24 + (- 6)

Answer

18

Your turnSame method, new numbers — try it before moving on.

Work out $(- 8) \times 3 - (- 20) \div 4$ .

Your answer

Order of operations

Brackets first, then Indices (powers and roots), then Division and Multiplication, then Addition and Subtraction — often remembered as BIDMAS.

Division and multiplication have $equal$ priority, and so do addition and subtraction: work left to right within each level. $12 \div 3 \times 2 = 8$ , not $2$ .

A fraction line acts like brackets around the top and bottom: $\frac{4 + 8}{3}$ means $(4 + 8) \div 3$ .

1Brackets:

7 - 2 = 5

2Index:

5^{2} = 25

3Multiply:

3 \times 25 = 75

4Add:

5 + 75

Answer

80

Your turnSame method, new numbers — try it before moving on.

Work out $40 - 2 \times (3 + 4)^{2} \div 7$ .

Your answer

Why this works

BIDMAS is a convention, not a law of nature — but because everyone uses the same one, a written calculation has exactly one meaning. Scientific calculators follow it too, which is why typing a calculation in one go works.

Checking with inverse operations

After a multiplication, divide back. If $368 \times 24 = 8832$ , then $8832 \div 24$ should give $368$ .

An estimate is an equally useful check. $368 \times 24 \approx 400 \times 20 = 8000$ , so $8832$ is reasonable while $883.2$ or $88320$ are not.

Tip — On the non-calculator paper, write a one-line estimate beside long calculations. It catches misplaced decimal points before they cost marks.

Think like an examiner

Show the method for long multiplication and division — method marks are available even with an arithmetic slip.
Work left to right within the same priority level.
Include units and interpret the answer in context for word problems.

Operations

a - (- b) = a + b

Subtracting a negative.

(- a) \times (- b) = ab

Same signs give a positive.

B, I, then D and M, then A and S

Order of operations.

Watch out for these

Working out

10 - 4 + 3

10 - 7 = 3

Addition and subtraction go left to right:

6 + 3 = 9

Writing

(- 3)^{2} = - 9

The bracket is squared:

(- 3) \times (- 3) = 9

Placing the decimal point without estimating:

2.4 \times 0.3 = 7.2

An estimate of about

0.6

shows the answer is

0.72

Thinking multiplication always comes before division.

They have equal priority; go left to right.

Stretch yourself

Insert brackets to make each statement true: (a) $6 + 4 \times 5 - 3 = 20$ (b) $6 + 4 \times 5 - 3 = 47$ .

Hint — Try bracketing different pairs and evaluating. One target needs the subtraction done early; the other needs the addition done early.

Questions students ask

Is it BIDMAS or BODMAS?

Both mean the same thing: "Indices" and "Orders" are two names for powers and roots.

How do I divide by a decimal without a calculator?

Multiply both numbers by 10, 100 or 1000 until the divisor is a whole number, then divide as normal.

What is

- 5 - 3

Start at

- 5

and move 3 further left:

- 8

Key takeaways

Use place-value methods for long multiplication and division.
Scale both numbers to divide by a decimal.
Same signs give positive, different signs give negative, for $\times$ and $\div$ .
BIDMAS, with left-to-right within equal priorities.
Check with inverse operations and estimates.

Exam-style questions

Practise it the way it is examined

3 original questions · 6 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.

Question 1Grade 22 marks

Work out $1845 \div 15$ .[2]

Question 2Grade 32 marks

596 people are going on a trip. Each coach holds 48 people.

How many coaches are needed?[2]

Question 3Grade 42 marks

Work out $(- 3)^{2} - 4 \times (- 2) \times 5$ .[2]

Unlimited practice

Skill drill

A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.

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Real past-paper questions on The Four Operations, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.

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The Four Operations

Written multiplication and division

Negative numbers

Order of operations

Checking with inverse operations

Practise it the way it is examined

Skill drill

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Related topics

The Four Operations

Written multiplication and division

Negative numbers

Order of operations

Checking with inverse operations

Practise it the way it is examined

Skill drill

Practise this topic

Related topics